Via Condotti and it's surrounding streets (located in front of Piazza di Spagna) contain most of the big names in fashion, accessories, jewellery and luxury goods. Here you will find Gucci, Prada, Christian Dior and alike.
Via del Corso is where you will find mid-range clothes, shoes etc... Here you will find stores like Miss Sixty, Diseal etc..
Should you wish to venture out of the centre take the metro A to Subaugusta. Here you will find a small shopping centre but also Via Tuscolana, a long road full of mid-range to inexpensive shops. There are many zones like this in Rome so if you have the time, move around the city a bit and discover them. It'll be worth your while.
There are also several markets in Rome worth visiting. Porta Portese is the largest and takes place on Sunday mornings. You will find bargains galore. Happy shopping!